Cayman Islands Species Abundance Analysis

Initial Data Wrangling

## # A tibble: 22,052 x 8
##    SPECIES_NAME   FISH_ID SCIENTIFIC_FAMILY  YEAR DIET   LOCATION MARINE_RESERVE
##    <chr>            <dbl> <chr>             <dbl> <chr>  <chr>    <chr>         
##  1 Blue Angelfish       1 Other              1998 Spong… CH       Yes           
##  2 Blue Angelfish       1 Other              1998 Spong… DG       Yes           
##  3 Blue Angelfish       1 Other              1998 Spong… SB       No            
##  4 Blue Angelfish       1 Other              1998 Spong… SC       No            
##  5 Blue Angelfish       1 Other              1998 Spong… TF       No            
##  6 Blue Angelfish       1 Other              2000 Spong… CP       Yes           
##  7 Blue Angelfish       1 Other              2000 Spong… DG       Yes           
##  8 Blue Angelfish       1 Other              2000 Spong… SC       No            
##  9 Blue Angelfish       1 Other              2000 Spong… CH       Yes           
## 10 Blue Angelfish       1 Other              2000 Spong… SB       No            
## # … with 22,042 more rows, and 1 more variable: DENSITY_INDEX <dbl>

Unique Datasets

Math

## [1] 16844

## [1] 1348

## [1] 1533

## [1] 411

Response Patterning

Variable Relationships:

Mathematical Summaries

Overall Summary Statistics for Eleven Dive Sites on Grand Cayman Island

Location	Mean Density Index	Standard Deviation	Standard Error	Sample Size
BB	0.4114386	0.8404847	0.0202777	1718
CH	0.3790222	0.8283496	0.0264742	979
CP	0.4427012	0.8590365	0.0173410	2454
CR	0.4992615	0.8826122	0.0212879	1719
DG	0.4622359	0.8855441	0.0170391	2701
ER	0.5200795	0.9229405	0.0340896	733
SB	0.4458110	0.8681177	0.0176143	2429
SC	0.3418897	0.7728271	0.0148786	2698
SH	0.4241696	0.8505619	0.0205328	1716
SV	0.4829153	0.8878970	0.0179273	2453
TF	0.4861403	0.8937834	0.0180498	2452

Overall Summary Statistics for Marine Reserve VS Non-Reserve Sites on Grand Cayman Island

Reserve Type	Mean Density Index	Standard Deviation	Standard Error	Sample Size
No	0.4199377	0.8451827	0.0087656	9297
Yes	0.4592603	0.8743441	0.0077418	12755

Overall Summary Statistics for Species Primary Diets on Grand Cayman Island

Diet	Mean Density Index	Standard Deviation	Standard Error	Sample Size
Algae	0.8157071	1.0791521	0.0211761	2597
Coral	1.1197525	1.0038735	0.0474286	448
Crustaceans	0.4475921	0.8598790	0.0108516	6279
Echinoids	0.3550889	0.7826984	0.0412518	360
Fish	0.3999007	0.7719094	0.0117715	4300
Sponges	0.4879182	0.7743653	0.0204134	1439
Unidentified	0.1628468	0.5479348	0.0074654	5387
Zooplankton	0.7284863	1.2434362	0.0352828	1242

Overall Summary Statistics Across Scientific Families on Grand Cayman Island

Family	Mean Density Index	Standard Deviation	Standard Error	Sample Size
Apogonidae	0.2023553	0.6248673	0.0268900	540
Carangidae	0.1822212	0.5963663	0.0181553	1079
Gobiidae	0.1782912	0.6100019	0.0151744	1616
Haemulidae	0.3256079	0.7707249	0.0203316	1437
Holocentridae	1.1331251	1.1666672	0.0505340	533
Labridae	0.4719138	0.8630698	0.0235422	1344
Lutjanidae	0.5678172	0.9033246	0.0301780	896
Other	0.4173957	0.8162026	0.0086644	8874
Pomacentridae	1.1796572	1.2673786	0.0360057	1239
Scaridae	0.7079198	1.0171146	0.0297866	1166
Serranidae	0.2995883	0.6482272	0.0124798	2698
Sparidae	0.2442227	0.7033578	0.0280224	630

Overall Summary Statistics of Density Index on Grand Cayman Island

Mean Density Index	Standard Deviation	Standard Error	Sample Size
0.4426821	0.8623694	0.0058072	22052

Non-Zero Summary Statistics for Eleven Dive Sites on Grand Cayman Island

Location	Mean Density Index	Standard Deviation	Standard Error	Sample Size
BB	1.910410	0.6446859	0.0335156	370
CH	1.922605	0.7155327	0.0515052	193
CP	1.844463	0.6990244	0.0288028	589
CR	1.803005	0.6796540	0.0311519	476
DG	1.903200	0.6970671	0.0272159	656
ER	1.906091	0.6915084	0.0488970	200
SB	1.893138	0.6780724	0.0283516	572
SC	1.844837	0.6706988	0.0299946	500
SH	1.885686	0.6778973	0.0345041	386
SV	1.871392	0.6753849	0.0268441	633
TF	1.883122	0.6806016	0.0270515	633

Non-Zero Summary Statistics for Marine Reserve VS Non-Reserve Sites on Grand Cayman Island

Reserve Type	Mean Density Index	Standard Deviation	Standard Error	Sample Size
No	1.881523	0.6711375	0.0147334	2075
Yes	1.869730	0.6892262	0.0123135	3133

Non-Zero Summary Statistics for Species Primary Diets on Grand Cayman Island

Diet	Mean Density Index	Standard Deviation	Standard Error	Sample Size
Algae	2.058689	0.6160146	0.0192036	1029
Coral	1.878836	0.5118014	0.0313217	267
Crustaceans	1.869881	0.6551331	0.0168986	1503
Echinoids	1.800451	0.7087813	0.0841169	71
Fish	1.640814	0.6391348	0.0197429	1048
Sponges	1.543108	0.5171518	0.0242445	455
Unidentified	1.758027	0.6611286	0.0295962	499
Zooplankton	2.692798	0.6498730	0.0354535	336

Non-Zero Summary Statistics Across Scientific Families on Grand Cayman Island

Family	Mean Density Index	Standard Deviation	Standard Error	Sample Size
Apogonidae	1.986762	0.5352753	0.0721765	55
Carangidae	1.908900	0.6560420	0.0646417	103
Gobiidae	2.072795	0.6319028	0.0535973	139
Haemulidae	1.925508	0.6568684	0.0421381	243
Holocentridae	2.220425	0.4988204	0.0302454	272
Labridae	1.781607	0.6914175	0.0366451	356
Lutjanidae	1.823528	0.5735640	0.0343384	279
Other	1.747980	0.6811335	0.0147968	2119
Pomacentridae	2.361220	0.6505770	0.0261489	619
Scaridae	1.984217	0.6046368	0.0296448	416
Serranidae	1.519341	0.5268009	0.0228397	532
Sparidae	2.051471	0.6689056	0.0772386	75

Non-Zero Summary Statistics of Density Index on Grand Cayman Island

Mean Density Index	Standard Deviation	Standard Error	Sample Size
1.874429	0.6820364	0.0094509	5208

Hypothesis Testing

## Levene's Test for Homogeneity of Variance (center = median)
##          Df F value    Pr(>F)    
## group    10  7.1728 2.151e-11 ***
##       22041                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Levene's Test for Homogeneity of Variance (center = median)
##          Df F value    Pr(>F)    
## group     1  11.186 0.0008255 ***
##       22050                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Levene's Test for Homogeneity of Variance (center = median)
##          Df F value    Pr(>F)    
## group     7  211.16 < 2.2e-16 ***
##       22044                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Levene's Test for Homogeneity of Variance (center = median)
##          Df F value    Pr(>F)    
## group    11  185.32 < 2.2e-16 ***
##       22040                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Levene's Test for Homogeneity of Variance (center = median)
##         Df F value Pr(>F)
## group   10  0.7767 0.6516
##       5197

## Levene's Test for Homogeneity of Variance (center = median)
##         Df F value Pr(>F)  
## group    1  3.4425 0.0636 .
##       5206                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Levene's Test for Homogeneity of Variance (center = median)
##         Df F value    Pr(>F)    
## group    7  9.5329 8.094e-12 ***
##       5200                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Levene's Test for Homogeneity of Variance (center = median)
##         Df F value    Pr(>F)    
## group   11  15.452 < 2.2e-16 ***
##       5196                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

##   NoZero_Levene_Test NoZero_Levene_PVals NoZero_Levene_Interpret
## 1               Diet           8.094e-12        Unequal Variance
## 2             Family             2.2e-16        Unequal Variance
## 3           Location              0.6516          Equal Variance
## 4            Reserve              0.0636          Equal Variance

Summary of Levene Test Results

Test Variable	Resulting P-Value	Interpretation
Diet	2.2e-16	Unequal Variance
Family	2.2e-16	Unequal Variance
Location	2.151e-11	Unequal Variance
Reserve	0.0008255	Unequal Variance

Non-Zero Data Summary of Levene Test Results

Test Variable	Resulting P-Value	Interpretation
Diet	8.094e-12	Unequal Variance
Family	2.2e-16	Unequal Variance
Location	0.6516	Equal Variance
Reserve	0.0636	Equal Variance

## 
##  One-way analysis of means (not assuming equal variances)
## 
## data:  DENSITY_INDEX and LOCATION
## F = 7.8556, num df = 10.0, denom df = 7185.7, p-value = 1.144e-12

## 
##  Welch Two Sample t-test
## 
## data:  DENSITY_INDEX by MARINE_RESERVE
## t = -3.3624, df = 20405, p-value = 0.0007742
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.06224556 -0.01639972
## sample estimates:
##  mean in group No mean in group Yes 
##         0.4199377         0.4592603

## 
##  One-way analysis of means (not assuming equal variances)
## 
## data:  DENSITY_INDEX and DIET
## F = 233.2, num df = 7.0, denom df = 3027.4, p-value < 2.2e-16

## 
##  One-way analysis of means (not assuming equal variances)
## 
## data:  DENSITY_INDEX and SCIENTIFIC_FAMILY
## F = 119.48, num df = 11.0, denom df = 4526.4, p-value < 2.2e-16

##               Df Sum Sq Mean Sq F value Pr(>F)
## LOCATION      10    5.4  0.5368   1.154  0.317
## Residuals   5197 2416.8  0.4650

## 
##  Two Sample t-test
## 
## data:  DENSITY_INDEX by MARINE_RESERVE
## t = 0.61085, df = 5206, p-value = 0.5413
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.02605401  0.04963955
## sample estimates:
##  mean in group No mean in group Yes 
##          1.881523          1.869731

## 
##  One-way analysis of means (not assuming equal variances)
## 
## data:  DENSITY_INDEX and DIET
## F = 137.34, num df = 7.00, denom df = 845.43, p-value < 2.2e-16

## 
##  One-way analysis of means (not assuming equal variances)
## 
## data:  DENSITY_INDEX and SCIENTIFIC_FAMILY
## F = 75.462, num df = 11.00, denom df = 734.19, p-value < 2.2e-16

##   NoZero_TANOVA_Test      NoZero_Test_Type NoZero_TANOVA_PVals
## 1               Diet           Welch ANOVA             2.2e-16
## 2             Family           Welch ANOVA             2.2e-16
## 3           Location        Standard ANOVA               0.317
## 4            Reserve Equal Variance T-Test              0.5413
##      NoZero_Result_Interpret
## 1 True Mean Difference Not 0
## 2 True Mean Difference Not 0
## 3   True Mean Difference = 0
## 4   True Mean Difference = 0

Summary of ANOVA and T-Test Results

Test Variable	Test Type	Resulting P-Value	Interpretation
Diet	Welch ANOVA	2.2e-16	True Mean Difference Not 0
Family	Welch ANOVA	2.2e-16	True Mean Difference Not 0
Location	Welch ANOVA	1.144e-12	True Mean Difference Not 0
Reserve	Welch T-Test	0.0007742	True Mean Difference Not 0

Non-Zero Data Summary of ANOVA and T-Test Results

Test Variable	Test Type	Resulting P-Value	Interpretation
Diet	Welch ANOVA	2.2e-16	True Mean Difference Not 0
Family	Welch ANOVA	2.2e-16	True Mean Difference Not 0
Location	Standard ANOVA	0.317	True Mean Difference = 0
Reserve	Equal Variance T-Test	0.5413	True Mean Difference = 0

Slope Investigation Plots

INTERACTION CHECK

MODELING WITH TWO PARTS

LOGISTIC REGRESSION PORTION

##  SCIENTIFIC_FAMILY       YEAR          DIET             LOCATION        
##  Length:22052       Min.   :1998   Length:22052       Length:22052      
##  Class :character   1st Qu.:2004   Class :character   Class :character  
##  Mode  :character   Median :2010   Mode  :character   Mode  :character  
##                     Mean   :2009                                        
##                     3rd Qu.:2014                                        
##                     Max.   :2018                                        
##  MARINE_RESERVE     DENSITY_INDEX   
##  Length:22052       Min.   :0.0000  
##  Class :character   1st Qu.:0.0000  
##  Mode  :character   Median :0.0000  
##                     Mean   :0.2362  
##                     3rd Qu.:0.0000  
##                     Max.   :1.0000

## [1] 16844

## 
## Call:
## glm(formula = DENSITY_INDEX ~ ., family = binomial(link = "logit"), 
##     data = CAYMAN_LOGISTIC_DATA)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -1.6089  -0.7642  -0.5179  -0.3165   2.5987  
## 
## Coefficients: (1 not defined because of singularities)
##                                  Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                    -98.832908   5.832728 -16.945  < 2e-16 ***
## SCIENTIFIC_FAMILYCarangidae     -0.979265   0.195182  -5.017 5.24e-07 ***
## SCIENTIFIC_FAMILYGobiidae        0.318873   0.182661   1.746 0.080862 .  
## SCIENTIFIC_FAMILYHaemulidae      0.058979   0.173020   0.341 0.733192    
## SCIENTIFIC_FAMILYHolocentridae   1.707774   0.184549   9.254  < 2e-16 ***
## SCIENTIFIC_FAMILYLabridae        0.787200   0.172325   4.568 4.92e-06 ***
## SCIENTIFIC_FAMILYLutjanidae      0.602563   0.179902   3.349 0.000810 ***
## SCIENTIFIC_FAMILYOther           0.465475   0.157401   2.957 0.003104 ** 
## SCIENTIFIC_FAMILYPomacentridae   1.497226   0.160466   9.331  < 2e-16 ***
## SCIENTIFIC_FAMILYScaridae        0.622229   0.174523   3.565 0.000363 ***
## SCIENTIFIC_FAMILYSerranidae      0.210358   0.167105   1.259 0.208090    
## SCIENTIFIC_FAMILYSparidae       -0.379678   0.204038  -1.861 0.062770 .  
## YEAR                             0.048537   0.002902  16.726  < 2e-16 ***
## DIETCoral                        1.160950   0.118867   9.767  < 2e-16 ***
## DIETCrustaceans                 -0.434950   0.081939  -5.308 1.11e-07 ***
## DIETEchinoids                   -0.674088   0.149795  -4.500 6.79e-06 ***
## DIETFish                        -0.085372   0.086043  -0.992 0.321101    
## DIETSponges                     -0.100493   0.086653  -1.160 0.246164    
## DIETUnidentified                -1.497794   0.088101 -17.001  < 2e-16 ***
## DIETZooplankton                 -0.630666   0.091735  -6.875 6.21e-12 ***
## LOCATIONCH                      -0.079906   0.105462  -0.758 0.448646    
## LOCATIONCP                       0.124029   0.079893   1.552 0.120558    
## LOCATIONCR                       0.204391   0.085011   2.404 0.016204 *  
## LOCATIONDG                       0.188154   0.078357   2.401 0.016339 *  
## LOCATIONER                       0.026480   0.109212   0.242 0.808418    
## LOCATIONSB                       0.143546   0.080298   1.788 0.073827 .  
## LOCATIONSC                      -0.197840   0.081186  -2.437 0.014815 *  
## LOCATIONSH                      -0.105803   0.087627  -1.207 0.227269    
## LOCATIONSV                       0.233321   0.079222   2.945 0.003228 ** 
## LOCATIONTF                       0.259324   0.079259   3.272 0.001068 ** 
## MARINE_RESERVEYes                      NA         NA      NA       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 24108  on 22051  degrees of freedom
## Residual deviance: 21575  on 22022  degrees of freedom
## AIC: 21635
## 
## Number of Fisher Scoring iterations: 5

## 
## Call:
## glm(formula = DENSITY_INDEX ~ SCIENTIFIC_FAMILY, family = binomial(link = "logit"), 
##     data = CAYMAN_LOGISTIC_DATA)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -1.1950  -0.7387  -0.6628  -0.4241   2.2151  
## 
## Coefficients:
##                                Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                    -2.17682    0.14227 -15.301  < 2e-16 ***
## SCIENTIFIC_FAMILYCarangidae    -0.07192    0.17599  -0.409 0.682793    
## SCIENTIFIC_FAMILYGobiidae      -0.18648    0.16765  -1.112 0.266011    
## SCIENTIFIC_FAMILYHaemulidae     0.58481    0.15873   3.684 0.000229 ***
## SCIENTIFIC_FAMILYHolocentridae  2.21810    0.16658  13.316  < 2e-16 ***
## SCIENTIFIC_FAMILYLabridae       1.15606    0.15512   7.453 9.14e-14 ***
## SCIENTIFIC_FAMILYLutjanidae     1.38316    0.15952   8.671  < 2e-16 ***
## SCIENTIFIC_FAMILYOther          1.01748    0.14443   7.045 1.86e-12 ***
## SCIENTIFIC_FAMILYPomacentridae  2.17520    0.15320  14.199  < 2e-16 ***
## SCIENTIFIC_FAMILYScaridae       1.58743    0.15485  10.251  < 2e-16 ***
## SCIENTIFIC_FAMILYSerranidae     0.77282    0.15027   5.143 2.71e-07 ***
## SCIENTIFIC_FAMILYSparidae       0.17534    0.18808   0.932 0.351224    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 24108  on 22051  degrees of freedom
## Residual deviance: 22825  on 22040  degrees of freedom
## AIC: 22849
## 
## Number of Fisher Scoring iterations: 4

## [1] 0.1015609

## [1] 0.168655

## [1] 0.5095238

## [1] 0.2642606

## [1] 0.3107019

## [1] 0.2382097

## [1] 0.4988

## [1] 0.3560454

## [1] 0.1966792

LINEAR MIXED EFFECT

How has density index values changed over time on Grand Cayman Island? How do density index values vary across dive sites?

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: DENSITY_INDEX ~ 1 + (1 | SPECIES_NAME)
##    Data: CAYMAN_NO_ZEROS
## 
## REML criterion at convergence: 8436.9
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.6607 -0.6235 -0.0347  0.6186  3.8503 
## 
## Random effects:
##  Groups       Name        Variance Std.Dev.
##  SPECIES_NAME (Intercept) 0.1947   0.4413  
##  Residual                 0.2653   0.5151  
## Number of obs: 5208, groups:  SPECIES_NAME, 231
## 
## Fixed effects:
##              Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept)   1.73686    0.03138 227.75030   55.35   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## [1] 0.4231606

Unconditional Growth Model

\[ Y_{ij}=\alpha_{0} + \beta_{0}\textrm{Year2013}_{ij}+u_{i}+v_{i}\textrm{Year2013}_{ij} + \epsilon_{ij} \]

where \(\epsilon_{ij}\sim N(0,\sigma^2)\) and

\[ \left[ \begin{array}{c} u_{i} \\ v_{i} \end{array} \right] \sim N \left( \left[ \begin{array}{c} 0 \\ 0 \end{array} \right], \left[ \begin{array}{cc} \sigma_{u}^{2} & \\ \rho_{uv}\sigma_{u}\sigma_{u} & \sigma_{v}^{2} \end{array} \right] \right) . \]

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: DENSITY_INDEX ~ YEAR1998 + (YEAR1998 | SPECIES_NAME)
##    Data: CAYMAN_NO_ZEROS
## 
## REML criterion at convergence: 8357.3
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.3173 -0.6166 -0.0355  0.6184  4.0456 
## 
## Random effects:
##  Groups       Name        Variance Std.Dev. Corr 
##  SPECIES_NAME (Intercept) 0.280071 0.52922       
##               YEAR1998    0.001437 0.03791  -0.58
##  Residual                 0.253967 0.50395       
## Number of obs: 5208, groups:  SPECIES_NAME, 231
## 
## Fixed effects:
##               Estimate Std. Error         df t value Pr(>|t|)    
## (Intercept)   1.854212   0.044437 166.901884  41.727  < 2e-16 ***
## YEAR1998     -0.015891   0.004004 114.793187  -3.969 0.000126 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##          (Intr)
## YEAR1998 -0.717
## optimizer (nloptwrap) convergence code: 0 (OK)
## Model failed to converge with max|grad| = 0.0151852 (tol = 0.002, component 1)

Building The Best Interpretation Model

## Single term additions
## 
## Model:
## DENSITY_INDEX ~ 1 + (1 | SPECIES_NAME)
##          Df    AIC    LRT  Pr(>Chi)    
## <none>      8437.8                     
## YEAR1998  1 8413.0 26.781 2.279e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Single term additions
## 
## Model:
## DENSITY_INDEX ~ YEAR1998 + (1 | SPECIES_NAME)
##                   Df    AIC    LRT  Pr(>Chi)    
## <none>               8413.0                     
## DIET               7 8382.2 44.889 1.437e-07 ***
## SCIENTIFIC_FAMILY 11 8376.3 58.711 1.608e-08 ***
## LOCATION          10 8418.8 14.245    0.1621    
## MARINE_RESERVE     1 8414.7  0.353    0.5525    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Single term additions
## 
## Model:
## DENSITY_INDEX ~ YEAR1998 + DIET + SCIENTIFIC_FAMILY + (1 | SPECIES_NAME)
##                            Df    AIC    LRT Pr(>Chi)    
## <none>                        8369.7                    
## YEAR1998:DIET               7 8376.9  6.809    0.449    
## YEAR1998:SCIENTIFIC_FAMILY 11 8345.4 46.336 2.82e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

##         df      AIC
## M4_LMER 33 8476.756
## M5_LMER 35 8431.912

##         df      AIC
## M3_LMER 22 8426.150
## M6_LMER 24 8365.182

##         df      AIC
## M5_LMER 35 8431.912
## M6_LMER 24 8365.182

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: DENSITY_INDEX ~ 1 + (1 | SPECIES_NAME)
##    Data: CAYMAN_NO_ZEROS
## 
## REML criterion at convergence: 8436.9
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.6607 -0.6235 -0.0347  0.6186  3.8503 
## 
## Random effects:
##  Groups       Name        Variance Std.Dev.
##  SPECIES_NAME (Intercept) 0.1947   0.4413  
##  Residual                 0.2653   0.5151  
## Number of obs: 5208, groups:  SPECIES_NAME, 231
## 
## Fixed effects:
##              Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept)   1.73686    0.03138 227.75030   55.35   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: DENSITY_INDEX ~ YEAR1998 + (YEAR1998 | SPECIES_NAME)
##    Data: CAYMAN_NO_ZEROS
## 
## REML criterion at convergence: 8357.3
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.3173 -0.6166 -0.0355  0.6184  4.0456 
## 
## Random effects:
##  Groups       Name        Variance Std.Dev. Corr 
##  SPECIES_NAME (Intercept) 0.280071 0.52922       
##               YEAR1998    0.001437 0.03791  -0.58
##  Residual                 0.253967 0.50395       
## Number of obs: 5208, groups:  SPECIES_NAME, 231
## 
## Fixed effects:
##               Estimate Std. Error         df t value Pr(>|t|)    
## (Intercept)   1.854212   0.044437 166.901884  41.727  < 2e-16 ***
## YEAR1998     -0.015891   0.004004 114.793187  -3.969 0.000126 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##          (Intr)
## YEAR1998 -0.717
## optimizer (nloptwrap) convergence code: 0 (OK)
## Model failed to converge with max|grad| = 0.0151852 (tol = 0.002, component 1)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: DENSITY_INDEX ~ YEAR1998 + DIET + SCIENTIFIC_FAMILY + (YEAR1998 |  
##     SPECIES_NAME)
##    Data: CAYMAN_NO_ZEROS
## 
## REML criterion at convergence: 8317.2
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.3381 -0.6207 -0.0392  0.6299  4.0419 
## 
## Random effects:
##  Groups       Name        Variance Std.Dev. Corr 
##  SPECIES_NAME (Intercept) 0.236515 0.48633       
##               YEAR1998    0.001482 0.03849  -0.67
##  Residual                 0.254096 0.50408       
## Number of obs: 5208, groups:  SPECIES_NAME, 231
## 
## Fixed effects:
##                                  Estimate Std. Error         df t value
## (Intercept)                      1.931554   0.242034 260.049362   7.981
## YEAR1998                        -0.016475   0.004034 114.664449  -4.084
## DIETCoral                       -0.004182   0.200072 157.441219  -0.021
## DIETCrustaceans                 -0.149696   0.134728 177.301377  -1.111
## DIETEchinoids                   -0.483322   0.243909 215.696344  -1.982
## DIETFish                        -0.298709   0.143481 180.233550  -2.082
## DIETSponges                     -0.351583   0.144637 171.021021  -2.431
## DIETUnidentified                -0.287404   0.134746 191.413786  -2.133
## DIETZooplankton                  0.257555   0.152225 183.685227   1.692
## SCIENTIFIC_FAMILYCarangidae      0.267641   0.273837 255.497620   0.977
## SCIENTIFIC_FAMILYGobiidae        0.416543   0.236083 262.136891   1.764
## SCIENTIFIC_FAMILYHaemulidae      0.134310   0.247698 263.625905   0.542
## SCIENTIFIC_FAMILYHolocentridae   0.492765   0.273202 219.550493   1.804
## SCIENTIFIC_FAMILYLabridae        0.076967   0.243285 246.818026   0.316
## SCIENTIFIC_FAMILYLutjanidae      0.164076   0.262790 241.225835   0.624
## SCIENTIFIC_FAMILYOther           0.039461   0.217699 267.321114   0.181
## SCIENTIFIC_FAMILYPomacentridae   0.500062   0.247137 258.940678   2.023
## SCIENTIFIC_FAMILYScaridae        0.040181   0.263504 236.749545   0.152
## SCIENTIFIC_FAMILYSerranidae     -0.075081   0.233853 254.686900  -0.321
## SCIENTIFIC_FAMILYSparidae        0.032139   0.294380 242.165587   0.109
##                                Pr(>|t|)    
## (Intercept)                    4.68e-14 ***
## YEAR1998                       8.22e-05 ***
## DIETCoral                        0.9833    
## DIETCrustaceans                  0.2680    
## DIETEchinoids                    0.0488 *  
## DIETFish                         0.0388 *  
## DIETSponges                      0.0161 *  
## DIETUnidentified                 0.0342 *  
## DIETZooplankton                  0.0924 .  
## SCIENTIFIC_FAMILYCarangidae      0.3293    
## SCIENTIFIC_FAMILYGobiidae        0.0788 .  
## SCIENTIFIC_FAMILYHaemulidae      0.5881    
## SCIENTIFIC_FAMILYHolocentridae   0.0727 .  
## SCIENTIFIC_FAMILYLabridae        0.7520    
## SCIENTIFIC_FAMILYLutjanidae      0.5330    
## SCIENTIFIC_FAMILYOther           0.8563    
## SCIENTIFIC_FAMILYPomacentridae   0.0441 *  
## SCIENTIFIC_FAMILYScaridae        0.8789    
## SCIENTIFIC_FAMILYSerranidae      0.7484    
## SCIENTIFIC_FAMILYSparidae        0.9132    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (nloptwrap) convergence code: 0 (OK)
## Model failed to converge with max|grad| = 0.0134851 (tol = 0.002, component 1)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: DENSITY_INDEX ~ YEAR1998 + DIET + SCIENTIFIC_FAMILY + YEAR1998 *  
##     SCIENTIFIC_FAMILY + (YEAR1998 | SPECIES_NAME)
##    Data: CAYMAN_NO_ZEROS
## 
## REML criterion at convergence: 8361.9
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.2876 -0.6155 -0.0400  0.6280  4.0287 
## 
## Random effects:
##  Groups       Name        Variance Std.Dev. Corr 
##  SPECIES_NAME (Intercept) 0.223818 0.47309       
##               YEAR1998    0.001315 0.03627  -0.65
##  Residual                 0.254134 0.50412       
## Number of obs: 5208, groups:  SPECIES_NAME, 231
## 
## Fixed effects:
##                                           Estimate Std. Error         df
## (Intercept)                               2.293987   0.407711 369.459496
## YEAR1998                                 -0.064930   0.044064 435.740900
## DIETCoral                                -0.001590   0.199777 157.720462
## DIETCrustaceans                          -0.141255   0.134558 177.720666
## DIETEchinoids                            -0.476373   0.243428 216.381090
## DIETFish                                 -0.293884   0.143249 180.574365
## DIETSponges                              -0.349200   0.144431 171.310290
## DIETUnidentified                         -0.283090   0.134521 191.656597
## DIETZooplankton                           0.253398   0.152083 184.158217
## SCIENTIFIC_FAMILYCarangidae              -0.489583   0.472019 288.984552
## SCIENTIFIC_FAMILYGobiidae                -0.303293   0.447512 307.309706
## SCIENTIFIC_FAMILYHaemulidae              -0.516095   0.440967 281.747513
## SCIENTIFIC_FAMILYHolocentridae            0.181904   0.453341 251.610551
## SCIENTIFIC_FAMILYLabridae                -0.278444   0.422658 298.472131
## SCIENTIFIC_FAMILYLutjanidae               0.160720   0.443705 279.833435
## SCIENTIFIC_FAMILYOther                   -0.349424   0.397607 327.079900
## SCIENTIFIC_FAMILYPomacentridae            0.114640   0.424717 307.098730
## SCIENTIFIC_FAMILYScaridae                -0.136882   0.437132 300.714423
## SCIENTIFIC_FAMILYSerranidae              -0.416355   0.414234 313.878389
## SCIENTIFIC_FAMILYSparidae                -0.308927   0.523212 266.910655
## YEAR1998:SCIENTIFIC_FAMILYCarangidae      0.093685   0.049787 332.517614
## YEAR1998:SCIENTIFIC_FAMILYGobiidae        0.089642   0.049401 409.214271
## YEAR1998:SCIENTIFIC_FAMILYHaemulidae      0.080383   0.047505 343.909396
## YEAR1998:SCIENTIFIC_FAMILYHolocentridae   0.040972   0.047919 294.589613
## YEAR1998:SCIENTIFIC_FAMILYLabridae        0.046633   0.046417 358.841600
## YEAR1998:SCIENTIFIC_FAMILYLutjanidae      0.003729   0.047315 320.827602
## YEAR1998:SCIENTIFIC_FAMILYOther           0.051300   0.044484 419.878598
## YEAR1998:SCIENTIFIC_FAMILYPomacentridae   0.051539   0.045756 351.506074
## YEAR1998:SCIENTIFIC_FAMILYScaridae        0.026291   0.046149 342.381198
## YEAR1998:SCIENTIFIC_FAMILYSerranidae      0.045119   0.045528 390.951745
## YEAR1998:SCIENTIFIC_FAMILYSparidae        0.045181   0.054649 312.773273
##                                         t value Pr(>|t|)    
## (Intercept)                               5.627 3.64e-08 ***
## YEAR1998                                 -1.474   0.1413    
## DIETCoral                                -0.008   0.9937    
## DIETCrustaceans                          -1.050   0.2953    
## DIETEchinoids                            -1.957   0.0516 .  
## DIETFish                                 -2.052   0.0417 *  
## DIETSponges                              -2.418   0.0167 *  
## DIETUnidentified                         -2.104   0.0366 *  
## DIETZooplankton                           1.666   0.0974 .  
## SCIENTIFIC_FAMILYCarangidae              -1.037   0.3005    
## SCIENTIFIC_FAMILYGobiidae                -0.678   0.4985    
## SCIENTIFIC_FAMILYHaemulidae              -1.170   0.2428    
## SCIENTIFIC_FAMILYHolocentridae            0.401   0.6886    
## SCIENTIFIC_FAMILYLabridae                -0.659   0.5105    
## SCIENTIFIC_FAMILYLutjanidae               0.362   0.7175    
## SCIENTIFIC_FAMILYOther                   -0.879   0.3801    
## SCIENTIFIC_FAMILYPomacentridae            0.270   0.7874    
## SCIENTIFIC_FAMILYScaridae                -0.313   0.7544    
## SCIENTIFIC_FAMILYSerranidae              -1.005   0.3156    
## SCIENTIFIC_FAMILYSparidae                -0.590   0.5554    
## YEAR1998:SCIENTIFIC_FAMILYCarangidae      1.882   0.0607 .  
## YEAR1998:SCIENTIFIC_FAMILYGobiidae        1.815   0.0703 .  
## YEAR1998:SCIENTIFIC_FAMILYHaemulidae      1.692   0.0915 .  
## YEAR1998:SCIENTIFIC_FAMILYHolocentridae   0.855   0.3932    
## YEAR1998:SCIENTIFIC_FAMILYLabridae        1.005   0.3157    
## YEAR1998:SCIENTIFIC_FAMILYLutjanidae      0.079   0.9372    
## YEAR1998:SCIENTIFIC_FAMILYOther           1.153   0.2495    
## YEAR1998:SCIENTIFIC_FAMILYPomacentridae   1.126   0.2608    
## YEAR1998:SCIENTIFIC_FAMILYScaridae        0.570   0.5693    
## YEAR1998:SCIENTIFIC_FAMILYSerranidae      0.991   0.3223    
## YEAR1998:SCIENTIFIC_FAMILYSparidae        0.827   0.4090    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (nloptwrap) convergence code: 0 (OK)
## Model failed to converge with max|grad| = 0.0168513 (tol = 0.002, component 1)

K Means Clustering

1998 K-MEANS

## K-means clustering with 4 clusters of sizes 3, 197, 45, 1
## 
## Cluster means:
##   MEAN_YEARLY_DI    N_Sites
## 1      3.3708185  -5.838370
## 2     -0.4338479   0.121128
## 3      1.6524260   0.121128
## 4      0.9964154 -11.797868
## 
## Clustering vector:
##   [1] 2 2 2 2 3 2 2 2 3 2 2 2 3 3 3 2 2 2 2 2 2 2 1 2 2 2 2 3 3 2 2 3 2 2 2 2 3
##  [38] 4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 3 2 3 2 2 1 2 2 3 3 3 2 2 2
##  [75] 2 2 2 2 2 2 3 3 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [112] 2 2 2 3 2 2 2 3 2 2 3 2 2 2 2 2 3 2 2 2 2 2 2 2 2 3 2 2 3 3 2 3 2 2 2 3 2
## [149] 2 2 2 2 2 2 3 3 2 2 2 2 2 2 2 2 2 2 3 2 2 2 3 2 2 2 2 3 2 2 2 2 2 2 2 2 2
## [186] 3 2 2 2 3 2 2 2 3 2 2 2 3 2 2 2 2 2 2 2 2 2 3 3 2 3 2 2 3 2 3 2 2 2 3 2 2
## [223] 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 3 2 2 2 2 3 2 2 3
## 
## Within cluster sum of squares by cluster:
## [1]  5.646235 17.475955 26.844551  0.000000
##  (between_SS / total_SS =  89.8 %)
## 
## Available components:
## 
## [1] "cluster"      "centers"      "totss"        "withinss"     "tot.withinss"
## [6] "betweenss"    "size"         "iter"         "ifault"

## [1]   3 197  45   1

## # A tibble: 1 x 4
##   MEAN_DI SD_DI MEAN_SITES SD_SITES
##     <dbl> <dbl>      <dbl>    <dbl>
## 1   0.413 0.701       4.98    0.168

##   MEAN_YEARLY_DI    N_Sites DI_CENTERS SITES_CENTERS CLUSTER_SIZE_98
## 1      3.3708185  -5.838370  2.7750663             4               3
## 2     -0.4338479   0.121128  0.1087986             5             197
## 3      1.6524260   0.121128  1.5708361             5              45
## 4      0.9964154 -11.797868  1.1111112             3               1

##           SPECIES_NAME MEAN_YEARLY_DI N_Sites cluster
## 1          Almaco Jack           0.00       5       2
## 2         Arrow Blenny           0.00       5       2
## 3   Atlantic Spadefish           0.40       5       2
## 4          Balloonfish           0.60       5       2
## 5 Banded Butterflyfish           1.25       5       3
## 6      Bandtail Puffer           0.00       5       2

2000 K-Means

## K-means clustering with 4 clusters of sizes 1, 13, 21, 211
## 
## Cluster means:
##   MEAN_YEARLY_DI      N_Sites
## 1      1.7907923 -15.62062947
## 2      3.2617558   0.06375767
## 3      1.6265220   0.06375767
## 4     -0.3713298   0.06375767
## 
## Clustering vector:
##   [1] 4 4 4 4 3 4 4 4 4 4 4 4 3 4 4 4 4 4 4 2 4 4 2 4 4 4 4 4 4 4 4 4 4 4 4 4 1
##  [38] 4 4 4 4 4 4 4 4 4 4 4 4 4 3 4 2 4 4 4 4 4 4 4 4 4 2 3 4 2 4 4 2 3 4 4 4 3
##  [75] 4 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [112] 3 4 4 3 4 4 3 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 4 2 4 4 3 4 4
## [149] 4 4 2 4 2 4 3 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4 2 4 4 4 4 2 4 4 4 4 4 4 4 4 4
## [186] 4 4 4 4 3 4 4 4 4 3 4 4 3 3 4 4 4 4 4 4 4 4 2 4 4 4 4 4 4 4 2 4 4 4 4 4 4
## [223] 4 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 4 3 4 4 4
## 
## Within cluster sum of squares by cluster:
## [1]  0.000000  2.656586  5.140756 11.037111
##  (between_SS / total_SS =  96.2 %)
## 
## Available components:
## 
## [1] "cluster"      "centers"      "totss"        "withinss"     "tot.withinss"
## [6] "betweenss"    "size"         "iter"         "ifault"

## [1]   1  13  21 211

## # A tibble: 1 x 4
##   MEAN_DI SD_DI MEAN_SITES SD_SITES
##     <dbl> <dbl>      <dbl>    <dbl>
## 1   0.338 0.705       7.99    0.191

##   MEAN_YEARLY_DI      N_Sites DI_CENTERS SITES_CENTERS CLUSTER_SIZE_00
## 1      1.7907923 -15.62062947 1.60000006             5               1
## 2      3.2617558   0.06375767 2.63654775             8              13
## 3      1.6265220   0.06375767 1.48424325             8              21
## 4     -0.3713298   0.06375767 0.07641189             8             211

##           SPECIES_NAME MEAN_YEARLY_DI N_Sites cluster
## 1          Almaco Jack          0.000       8       4
## 2         Arrow Blenny          0.375       8       4
## 3   Atlantic Spadefish          0.000       8       4
## 4          Balloonfish          0.375       8       4
## 5 Banded Butterflyfish          1.725       8       3
## 6      Bandtail Puffer          0.000       8       4

2002 K-Means

## K-means clustering with 4 clusters of sizes 28, 193, 1, 24
## 
## Cluster means:
##   MEAN_YEARLY_DI    N_Sites
## 1      2.2038192 -2.3407942
## 2     -0.4705805  0.3360832
## 3      3.7637425 -7.7224331
## 4      1.0563062  0.3500253
## 
## Clustering vector:
##   [1] 2 2 2 2 4 2 1 2 2 2 2 2 1 1 4 2 2 2 2 2 2 2 4 2 2 2 2 1 1 2 2 2 2 2 2 2 3
##  [38] 4 2 2 2 2 2 2 2 4 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 1 2 2 1 2 2 1 4 1 2 2 2
##  [75] 2 2 2 2 2 2 2 4 2 4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 4 2 2 2 2 2 2 1 2
## [112] 2 2 2 4 2 2 1 4 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 1 2 2 4 2 2 4 2 4 2 1 2
## [149] 2 4 2 2 2 2 4 4 2 2 2 2 2 2 2 2 2 2 4 2 2 2 1 2 2 2 2 1 2 2 2 2 2 2 2 2 2
## [186] 2 2 2 2 4 2 2 2 1 2 2 2 1 2 2 2 4 2 2 2 2 1 1 1 2 1 2 2 1 2 1 2 2 2 1 2 2
## [223] 2 2 2 2 2 2 4 2 2 2 2 2 2 2 4 4 2 2 2 2 4 2 2 1
## 
## Within cluster sum of squares by cluster:
## [1] 10.408610 15.595991  0.000000  6.523836
##  (between_SS / total_SS =  93.4 %)
## 
## Available components:
## 
## [1] "cluster"      "centers"      "totss"        "withinss"     "tot.withinss"
## [6] "betweenss"    "size"         "iter"         "ifault"

## [1]  28 193   1  24

## # A tibble: 1 x 4
##   MEAN_DI SD_DI MEAN_SITES SD_SITES
##     <dbl> <dbl>      <dbl>    <dbl>
## 1   0.432 0.749       6.87    0.372

##   MEAN_YEARLY_DI    N_Sites DI_CENTERS SITES_CENTERS CLUSTER_SIZE_02
## 1      2.2038192 -2.3407942 2.08224209      6.000000              28
## 2     -0.4705805  0.3360832 0.08018755      6.994819             193
## 3      3.7637425 -7.7224331 3.25000003      4.000000               1
## 4      1.0563062  0.3500253 1.22321432      7.000000              24

##           SPECIES_NAME MEAN_YEARLY_DI N_Sites cluster
## 1          Almaco Jack      0.0000000       7       2
## 2         Arrow Blenny      0.0000000       7       2
## 3   Atlantic Spadefish      0.0000000       7       2
## 4          Balloonfish      0.1428571       7       2
## 5 Banded Butterflyfish      1.4285714       7       4
## 6      Bandtail Puffer      0.1428571       7       2

2004 K-Means

## K-means clustering with 4 clusters of sizes 22, 202, 1, 21
## 
## Cluster means:
##   MEAN_YEARLY_DI      N_Sites
## 1      1.0491517   0.06375767
## 2     -0.4151812   0.06375767
## 3      1.3180506 -15.62062947
## 4      2.8317720   0.06375767
## 
## Clustering vector:
##   [1] 2 2 2 2 2 2 2 4 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 1 1 2 2 2 2 2 2 2 2 2
##  [38] 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 1 2 2 4 2 2 2 4 1 2 2 2 4 2 2 2 1 2 1 2 2
##  [75] 1 2 2 2 2 2 2 1 2 2 1 2 2 2 2 2 2 4 2 2 2 2 2 2 2 4 4 2 2 2 2 2 4 4 1 2 4
## [112] 2 4 2 2 2 2 1 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 1 2 4 4 2 2 1 1 4
## [149] 2 2 2 2 4 2 4 2 2 2 2 2 2 2 2 2 2 2 1 2 2 4 2 2 2 2 2 2 2 2 2 2 2 2 4 4 2
## [186] 2 2 2 2 2 2 2 2 2 2 2 2 1 1 2 2 2 2 2 2 2 2 2 2 2 2 4 2 2 2 4 2 2 2 1 2 2
## [223] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 3 2
## 
## Within cluster sum of squares by cluster:
## [1] 4.715479 5.434402 0.000000 5.679612
##  (between_SS / total_SS =  96.8 %)
## 
## Available components:
## 
## [1] "cluster"      "centers"      "totss"        "withinss"     "tot.withinss"
## [6] "betweenss"    "size"         "iter"         "ifault"

## [1]  22 202   1  21

## # A tibble: 1 x 4
##   MEAN_DI SD_DI MEAN_SITES SD_SITES
##     <dbl> <dbl>      <dbl>    <dbl>
## 1   0.317 0.670       6.00   0.0638

##   MEAN_YEARLY_DI      N_Sites DI_CENTERS SITES_CENTERS CLUSTER_SIZE_04
## 1      1.0491517   0.06375767 1.00245042             7              22
## 2     -0.4151812   0.06375767 0.03916642             7             202
## 3      1.3180506 -15.62062947 1.17934056             6               1
## 4      2.8317720   0.06375767 2.17511388             7              21

##           SPECIES_NAME MEAN_YEARLY_DI N_Sites cluster
## 1          Almaco Jack      0.0000000       6       2
## 2         Arrow Blenny      0.0000000       6       2
## 3   Atlantic Spadefish      0.0000000       6       2
## 4          Balloonfish      0.0000000       6       2
## 5 Banded Butterflyfish      0.3333333       6       2
## 6      Bandtail Puffer      0.0000000       6       2

2006 K-Means

## K-means clustering with 4 clusters of sizes 1, 201, 25, 19
## 
## Cluster means:
##   MEAN_YEARLY_DI      N_Sites
## 1      1.4543713 -15.62062947
## 2     -0.4215216   0.06375767
## 3      1.1259748   0.06375767
## 4      2.9011636   0.06375767
## 
## Clustering vector:
##   [1] 2 2 2 2 2 2 2 4 2 2 3 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2
##  [38] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 2 2 2 4 2 2 4 3 4 2 2 2 4 2 2 2 2
##  [75] 3 2 2 2 2 2 2 3 2 2 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 3 4 2 2 2 2 2 4 4 3 3 4
## [112] 2 4 2 2 2 2 4 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 3 2 3 2 3 2 4 3 2 2 3 2 4
## [149] 2 2 2 2 4 3 4 2 2 2 2 2 2 2 2 2 2 2 3 2 2 3 3 2 2 2 2 2 2 2 2 2 2 2 4 2 2
## [186] 2 2 2 2 2 2 2 2 2 2 2 2 4 3 2 2 2 2 2 2 2 2 2 2 2 2 4 2 2 2 3 2 2 2 2 2 2
## [223] 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 3 2 2 1 2
## 
## Within cluster sum of squares by cluster:
## [1] 0.000000 5.995451 5.379587 4.182251
##  (between_SS / total_SS =  96.8 %)
## 
## Available components:
## 
## [1] "cluster"      "centers"      "totss"        "withinss"     "tot.withinss"
## [6] "betweenss"    "size"         "iter"         "ifault"

## [1]   1 201  25  19

## # A tibble: 1 x 4
##   MEAN_DI SD_DI MEAN_SITES SD_SITES
##     <dbl> <dbl>      <dbl>    <dbl>
## 1   0.324 0.661       8.00   0.0638

##   MEAN_YEARLY_DI      N_Sites DI_CENTERS SITES_CENTERS CLUSTER_SIZE_06
## 1      1.4543713 -15.62062947 1.28571423             7               1
## 2     -0.4215216   0.06375767 0.04560531             8             201
## 3      1.1259748   0.06375767 1.06861900             8              25
## 4      2.9011636   0.06375767 2.24215477             8              19

##           SPECIES_NAME MEAN_YEARLY_DI N_Sites cluster
## 1          Almaco Jack          0.000       8       2
## 2         Arrow Blenny          0.000       8       2
## 3   Atlantic Spadefish          0.125       8       2
## 4          Balloonfish          0.000       8       2
## 5 Banded Butterflyfish          0.125       8       2
## 6      Bandtail Puffer          0.000       8       2

2008 K-Means

## K-means clustering with 4 clusters of sizes 1, 27, 195, 23
## 
## Cluster means:
##   MEAN_YEARLY_DI      N_Sites
## 1      2.3529504 -15.62062947
## 2      0.9355029   0.06375767
## 3     -0.4532149   0.06375767
## 4      2.6419727   0.06375767
## 
## Clustering vector:
##   [1] 3 3 3 3 2 3 3 4 3 3 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
##  [38] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 3 3 4 3 3 3 4 3 2 3 2 4 3 3 3 4 3 2 3 3
##  [75] 3 3 3 3 3 3 3 4 3 3 2 2 2 3 3 3 2 4 3 3 3 3 3 3 3 2 4 3 3 3 3 3 4 4 2 3 4
## [112] 3 4 3 3 3 3 1 3 3 3 3 3 3 3 3 3 4 3 3 3 3 3 3 3 3 3 2 3 2 3 4 2 3 3 2 2 4
## [149] 3 3 2 3 4 2 4 3 3 2 3 3 3 3 3 2 3 3 2 3 3 4 3 3 3 3 3 3 3 3 3 3 3 3 4 2 3
## [186] 3 3 3 3 3 3 3 3 2 3 3 3 4 2 3 3 3 3 3 3 3 3 3 3 3 3 4 3 2 3 4 3 3 3 3 3 3
## [223] 2 3 3 3 3 3 3 3 3 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3
## 
## Within cluster sum of squares by cluster:
## [1] 0.000000 3.924964 5.122044 6.192959
##  (between_SS / total_SS =  96.9 %)
## 
## Available components:
## 
## [1] "cluster"      "centers"      "totss"        "withinss"     "tot.withinss"
## [6] "betweenss"    "size"         "iter"         "ifault"

## [1]   1  27 195  23

## # A tibble: 1 x 4
##   MEAN_DI SD_DI MEAN_SITES SD_SITES
##     <dbl> <dbl>      <dbl>    <dbl>
## 1   0.373 0.725       8.00   0.0638

##   MEAN_YEARLY_DI      N_Sites DI_CENTERS SITES_CENTERS CLUSTER_SIZE_08
## 1      2.3529504 -15.62062947 2.08027203             7               1
## 2      0.9355029   0.06375767 1.05204472             8              27
## 3     -0.4532149   0.06375767 0.04465814             8             195
## 4      2.6419727   0.06375767 2.28993105             8              23

##           SPECIES_NAME MEAN_YEARLY_DI N_Sites cluster
## 1          Almaco Jack       0.000000       8       3
## 2         Arrow Blenny       0.000000       8       3
## 3   Atlantic Spadefish       0.000000       8       3
## 4          Balloonfish       0.000000       8       3
## 5 Banded Butterflyfish       1.627083       8       2
## 6      Bandtail Puffer       0.000000       8       3

2010 K-Means

## K-means clustering with 4 clusters of sizes 160, 30, 5, 51
## 
## Cluster means:
##   MEAN_YEARLY_DI   N_Sites
## 1     -0.6043733  0.136227
## 2      2.1358098  0.136227
## 3      1.4296039 -6.566141
## 4      0.4995571  0.136227
## 
## Clustering vector:
##   [1] 1 4 1 1 1 4 1 2 1 1 1 1 1 4 1 1 1 1 4 3 1 1 1 4 1 1 2 2 1 1 4 1 1 1 1 4 1
##  [38] 1 1 4 1 1 1 1 1 1 1 1 1 1 4 4 4 2 1 1 2 1 1 1 2 2 4 4 4 2 1 1 1 4 2 4 1 3
##  [75] 1 1 1 4 4 1 4 4 1 4 3 4 1 1 1 1 1 4 1 1 1 1 1 1 1 2 2 2 4 4 4 1 2 2 4 4 2
## [112] 1 2 1 4 2 1 4 1 1 1 1 1 1 4 1 1 2 1 1 1 1 1 1 1 1 1 4 1 4 1 2 4 1 1 2 4 2
## [149] 1 1 3 1 2 4 2 1 1 1 1 1 1 1 1 1 1 1 4 1 1 4 1 1 1 1 1 2 1 1 1 1 1 1 2 4 1
## [186] 1 2 1 1 4 1 1 1 4 1 1 1 2 2 4 1 1 1 1 1 1 1 4 1 1 1 2 1 1 1 2 1 1 1 4 1 1
## [223] 4 1 1 1 1 1 4 1 4 1 1 1 4 4 1 1 1 1 1 4 4 1 3 1
## 
## Within cluster sum of squares by cluster:
## [1]  4.171866  7.603094 32.798465  7.143601
##  (between_SS / total_SS =  89.4 %)
## 
## Available components:
## 
## [1] "cluster"      "centers"      "totss"        "withinss"     "tot.withinss"
## [6] "betweenss"    "size"         "iter"         "ifault"

## [1] 160  30   5  51

## # A tibble: 1 x 4
##   MEAN_DI SD_DI MEAN_SITES SD_SITES
##     <dbl> <dbl>      <dbl>    <dbl>
## 1   0.522 0.749       7.98    0.179

##   MEAN_YEARLY_DI   N_Sites DI_CENTERS SITES_CENTERS CLUSTER_SIZE_10
## 1     -0.6043733  0.136227  0.0759519      8.997364             160
## 2      2.1358098  0.136227  2.1001345      8.997364              30
## 3      1.4296039 -6.566141  1.5784578      7.727063               5
## 4      0.4995571  0.136227  0.8914290      8.997364              51

##           SPECIES_NAME MEAN_YEARLY_DI N_Sites cluster
## 1          Almaco Jack         0.0000       8       1
## 2         Arrow Blenny         0.5625       8       4
## 3   Atlantic Spadefish         0.0000       8       1
## 4          Balloonfish         0.0000       8       1
## 5 Banded Butterflyfish         0.1250       8       1
## 6      Bandtail Puffer         0.6250       8       4

2012 K-Means

## K-means clustering with 4 clusters of sizes 2, 40, 42, 162
## 
## Cluster means:
##   MEAN_YEARLY_DI      N_Sites
## 1      0.8621329 -11.02288823
## 2      0.4481398   0.09035154
## 3      1.8956548   0.09035154
## 4     -0.6127615   0.09035154
## 
## Clustering vector:
##   [1] 4 4 4 4 2 4 2 3 2 4 4 4 4 2 4 4 4 3 3 2 4 4 4 4 4 4 3 3 4 4 4 4 4 4 4 4 4
##  [38] 4 4 2 4 4 4 4 4 4 4 4 4 4 2 4 3 2 4 4 3 4 4 4 3 4 3 3 2 3 4 4 4 3 4 4 4 1
##  [75] 2 2 4 4 4 4 2 2 4 2 3 2 2 4 4 4 4 3 4 4 4 4 4 4 3 3 3 3 3 2 2 4 3 3 3 3 3
## [112] 2 3 4 4 4 4 3 4 4 4 4 4 4 2 4 4 3 4 4 4 4 4 2 2 4 4 2 4 2 4 3 2 4 4 3 2 3
## [149] 4 4 2 4 3 2 3 4 4 4 4 4 4 4 4 2 4 4 2 4 4 2 2 3 4 4 4 2 4 4 4 4 4 4 3 2 4
## [186] 4 4 4 4 4 4 4 4 2 4 4 4 3 3 4 4 4 2 4 4 4 4 3 3 4 2 3 4 4 4 3 2 4 4 4 4 4
## [223] 4 4 4 4 4 4 4 4 4 4 4 4 4 2 4 4 2 4 4 3 4 4 1 3
## 
## Within cluster sum of squares by cluster:
## [1]  4.734627  5.010843 11.221328  2.758980
##  (between_SS / total_SS =  95.2 %)
## 
## Available components:
## 
## [1] "cluster"      "centers"      "totss"        "withinss"     "tot.withinss"
## [6] "betweenss"    "size"         "iter"         "ifault"

## [1]   2  40  42 162

## # A tibble: 1 x 4
##   MEAN_DI SD_DI MEAN_SITES SD_SITES
##     <dbl> <dbl>      <dbl>    <dbl>
## 1   0.550 0.813       9.99   0.0900

##   MEAN_YEARLY_DI      N_Sites DI_CENTERS SITES_CENTERS CLUSTER_SIZE_12
## 1      0.8621329 -11.02288823 1.25092598             9               2
## 2      0.4481398   0.09035154 0.91433932            10              40
## 3      1.8956548   0.09035154 2.09120475            10              42
## 4     -0.6127615   0.09035154 0.05180039            10             162

##           SPECIES_NAME MEAN_YEARLY_DI N_Sites cluster
## 1          Almaco Jack            0.0      10       4
## 2         Arrow Blenny            0.0      10       4
## 3   Atlantic Spadefish            0.0      10       4
## 4          Balloonfish            0.1      10       4
## 5 Banded Butterflyfish            0.6      10       2
## 6      Bandtail Puffer            0.2      10       4

2014 K-Means

## K-means clustering with 4 clusters of sizes 1, 169, 36, 40
## 
## Cluster means:
##   MEAN_YEARLY_DI      N_Sites
## 1     -0.6386303 -14.61611025
## 2     -0.5562018   0.10256919
## 3      2.1321229  -0.13106064
## 4      0.4470079   0.05000248
## 
## Clustering vector:
##   [1] 2 2 2 2 3 2 3 2 2 2 2 2 3 3 4 2 2 4 2 2 2 2 3 2 2 2 2 3 3 2 2 3 2 2 2 2 3
##  [38] 3 2 2 2 2 2 2 2 4 3 2 3 2 2 4 2 4 2 2 2 2 2 2 2 2 3 2 2 3 4 2 3 4 3 2 2 2
##  [75] 2 2 2 4 2 2 3 4 2 4 2 2 2 2 2 4 2 2 4 2 2 2 2 2 4 2 2 2 2 2 4 2 3 2 2 4 4
## [112] 2 2 4 4 2 2 4 4 2 2 3 2 2 2 2 2 4 2 2 2 2 2 2 4 2 3 2 2 4 3 2 3 2 2 2 4 3
## [149] 2 2 2 2 2 2 3 4 2 2 2 2 2 2 2 2 2 2 4 2 2 2 3 2 4 2 2 3 2 2 3 2 2 2 2 2 2
## [186] 1 2 3 2 4 2 2 2 4 2 2 2 4 2 2 2 4 2 3 2 2 4 3 3 2 4 2 2 4 2 3 2 2 2 4 2 2
## [223] 2 2 4 4 2 2 3 4 4 2 2 2 2 2 3 2 2 2 2 4 3 2 2 3
## 
## Within cluster sum of squares by cluster:
## [1]  0.000000  3.921278 36.422495  9.192672
##  (between_SS / total_SS =  89.9 %)
## 
## Available components:
## 
## [1] "cluster"      "centers"      "totss"        "withinss"     "tot.withinss"
## [6] "betweenss"    "size"         "iter"         "ifault"

## [1]   1 169  36  40

## # A tibble: 1 x 4
##   MEAN_DI SD_DI MEAN_SITES SD_SITES
##     <dbl> <dbl>      <dbl>    <dbl>
## 1   0.507 0.794       9.95    0.476

##   MEAN_YEARLY_DI      N_Sites   DI_CENTERS SITES_CENTERS CLUSTER_SIZE_14
## 1     -0.6386303 -14.61611025 6.968117e-09      3.000001               1
## 2     -0.5562018   0.10256919 6.548324e-02     10.000000             169
## 3      2.1321229  -0.13106064 2.201156e+00      9.888889              36
## 4      0.4470079   0.05000248 8.624584e-01      9.975000              40

##           SPECIES_NAME MEAN_YEARLY_DI N_Sites cluster
## 1          Almaco Jack       0.000000      10       2
## 2         Arrow Blenny       0.000000      10       2
## 3   Atlantic Spadefish       0.000000      10       2
## 4          Balloonfish       0.450000      10       2
## 5 Banded Butterflyfish       2.119048      10       3
## 6      Bandtail Puffer       0.000000      10       2

2016 K-Means

## K-means clustering with 4 clusters of sizes 3, 10, 20, 213
## 
## Cluster means:
##   MEAN_YEARLY_DI   N_Sites
## 1      2.6275241 -8.981689
## 2      3.7641263  0.110885
## 3      1.3479576  0.110885
## 4     -0.3402957  0.110885
## 
## Clustering vector:
##   [1] 4 4 4 3 2 4 4 4 4 4 4 4 3 2 4 4 4 4 4 4 4 4 2 4 4 4 4 1 2 4 4 4 4 4 4 4 4
##  [38] 1 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 4 4 2 4 4 2 3 2 4 4 4
##  [75] 4 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4
## [112] 4 4 4 3 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 4 4 3 4 4 4 4 4 4 3 4
## [149] 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 4 3 4 4 1 4 4 4 4 4 4 4 4 4
## [186] 4 4 4 4 3 4 4 4 3 4 4 4 3 4 4 4 4 4 4 4 4 4 2 2 4 4 4 4 3 4 4 4 4 4 4 4 4
## [223] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4
## 
## Within cluster sum of squares by cluster:
## [1] 6.775944 4.386883 5.016937 5.416670
##  (between_SS / total_SS =  95.6 %)
## 
## Available components:
## 
## [1] "cluster"      "centers"      "totss"        "withinss"     "tot.withinss"
## [6] "betweenss"    "size"         "iter"         "ifault"

## [1]   3  10  20 213

## # A tibble: 1 x 4
##   MEAN_DI SD_DI MEAN_SITES SD_SITES
##     <dbl> <dbl>      <dbl>    <dbl>
## 1   0.193 0.491       9.99    0.110

##   MEAN_YEARLY_DI   N_Sites DI_CENTERS SITES_CENTERS CLUSTER_SIZE_16
## 1      2.6275241 -8.981689  1.4839505             9               3
## 2      3.7641263  0.110885  2.0423332            10              10
## 3      1.3479576  0.110885  0.8553333            10              20
## 4     -0.3402957  0.110885  0.0259390            10             213

##           SPECIES_NAME MEAN_YEARLY_DI N_Sites cluster
## 1          Almaco Jack      0.0000000      10       4
## 2         Arrow Blenny      0.0000000      10       4
## 3   Atlantic Spadefish      0.0000000      10       4
## 4          Balloonfish      0.8333333      10       3
## 5 Banded Butterflyfish      1.8500000      10       2
## 6      Bandtail Puffer      0.0000000      10       4

2018 K-Means

## K-means clustering with 4 clusters of sizes 53, 117, 72, 4
## 
## Cluster means:
##   MEAN_YEARLY_DI     N_Sites
## 1      1.5649029  0.02820007
## 2     -0.8156263  0.12886692
## 3      0.1110118  0.12455030
## 4      1.1238945 -6.38491389
## 
## Clustering vector:
##   [1] 2 2 2 3 1 3 1 2 3 1 2 2 1 1 3 3 2 3 1 2 2 3 1 2 3 3 2 1 1 2 2 1 3 2 2 2 1
##  [38] 4 2 2 3 2 2 2 3 1 1 2 1 3 2 3 2 3 2 2 2 2 2 1 1 3 1 1 2 1 2 2 1 1 1 2 2 2
##  [75] 2 1 2 3 3 2 1 3 2 3 3 2 3 3 2 3 2 2 3 3 1 2 2 2 1 2 3 2 3 2 3 2 1 1 3 4 3
## [112] 2 3 3 1 3 2 1 3 3 3 1 3 2 3 2 2 3 2 2 2 2 2 2 3 2 1 2 3 1 3 3 3 3 2 2 1 1
## [149] 3 2 1 2 4 1 1 3 2 2 2 2 2 3 2 2 3 2 3 2 3 2 1 2 3 2 2 1 2 2 1 2 2 3 2 2 2
## [186] 2 2 2 3 1 2 3 2 1 2 2 2 1 2 2 2 3 2 3 2 2 3 1 1 3 1 3 2 1 2 1 3 2 2 3 2 3
## [223] 2 2 3 3 2 2 1 3 3 2 2 2 3 2 1 4 2 3 2 3 1 3 2 1
## 
## Within cluster sum of squares by cluster:
## [1] 31.56526 16.01667 15.58508 47.09595
##  (between_SS / total_SS =  77.5 %)
## 
## Available components:
## 
## [1] "cluster"      "centers"      "totss"        "withinss"     "tot.withinss"
## [6] "betweenss"    "size"         "iter"         "ifault"

## [1]  53 117  72   4

## [1]  53 117  72   4

## # A tibble: 1 x 4
##   MEAN_DI SD_DI MEAN_SITES SD_SITES
##     <dbl> <dbl>      <dbl>    <dbl>
## 1   0.833 0.838       9.91    0.495

##   MEAN_YEARLY_DI     N_Sites DI_CENTERS SITES_CENTERS CLUSTER_SIZE_18
## 1      1.5649029  0.02820007  2.1440958      9.924528              53
## 2     -0.8156263  0.12886692  0.1493352      9.974359             117
## 3      0.1110118  0.12455030  0.9258102      9.972222              72
## 4      1.1238945 -6.38491389  1.7745536      6.750000               4

##           SPECIES_NAME MEAN_YEARLY_DI N_Sites cluster
## 1          Almaco Jack       0.300000      10       2
## 2         Arrow Blenny       0.100000      10       2
## 3   Atlantic Spadefish       0.400000      10       2
## 4          Balloonfish       1.500000      10       3
## 5 Banded Butterflyfish       2.103571      10       1
## 6      Bandtail Puffer       0.700000      10       3

Visualize Optimal K Plots

Visualize Yearly Clusters

Unscaled Cluster Centers

##   DI_CENTERS SITES_CENTERS MEAN_YEARLY_DI    N_Sites
## 1  2.7750663             4      3.3708185  -5.838370
## 2  0.1087986             5     -0.4338479   0.121128
## 3  1.5708361             5      1.6524260   0.121128
## 4  1.1111112             3      0.9964154 -11.797868

##   DI_CENTERS SITES_CENTERS MEAN_YEARLY_DI      N_Sites
## 1 1.60000006             5      1.7907923 -15.62062947
## 2 2.63654775             8      3.2617558   0.06375767
## 3 1.48424325             8      1.6265220   0.06375767
## 4 0.07641189             8     -0.3713298   0.06375767

##   DI_CENTERS SITES_CENTERS MEAN_YEARLY_DI    N_Sites
## 1 2.08224209      6.000000      2.2038192 -2.3407942
## 2 0.08018755      6.994819     -0.4705805  0.3360832
## 3 3.25000003      4.000000      3.7637425 -7.7224331
## 4 1.22321432      7.000000      1.0563062  0.3500253

##   DI_CENTERS SITES_CENTERS MEAN_YEARLY_DI      N_Sites
## 1 1.00245042             7      1.0491517   0.06375767
## 2 0.03916642             7     -0.4151812   0.06375767
## 3 1.17934056             6      1.3180506 -15.62062947
## 4 2.17511388             7      2.8317720   0.06375767

##   DI_CENTERS SITES_CENTERS MEAN_YEARLY_DI      N_Sites
## 1 1.28571423             7      1.4543713 -15.62062947
## 2 0.04560531             8     -0.4215216   0.06375767
## 3 1.06861900             8      1.1259748   0.06375767
## 4 2.24215477             8      2.9011636   0.06375767

##   DI_CENTERS SITES_CENTERS MEAN_YEARLY_DI      N_Sites
## 1 2.08027203             7      2.3529504 -15.62062947
## 2 1.05204472             8      0.9355029   0.06375767
## 3 0.04465814             8     -0.4532149   0.06375767
## 4 2.28993105             8      2.6419727   0.06375767

##   DI_CENTERS SITES_CENTERS MEAN_YEARLY_DI   N_Sites
## 1  0.0759519      8.997364     -0.6043733  0.136227
## 2  2.1001345      8.997364      2.1358098  0.136227
## 3  1.5784578      7.727063      1.4296039 -6.566141
## 4  0.8914290      8.997364      0.4995571  0.136227

##   DI_CENTERS SITES_CENTERS MEAN_YEARLY_DI      N_Sites
## 1 1.25092598             9      0.8621329 -11.02288823
## 2 0.91433932            10      0.4481398   0.09035154
## 3 2.09120475            10      1.8956548   0.09035154
## 4 0.05180039            10     -0.6127615   0.09035154

##     DI_CENTERS SITES_CENTERS MEAN_YEARLY_DI      N_Sites
## 1 6.968117e-09      3.000001     -0.6386303 -14.61611025
## 2 6.548324e-02     10.000000     -0.5562018   0.10256919
## 3 2.201156e+00      9.888889      2.1321229  -0.13106064
## 4 8.624584e-01      9.975000      0.4470079   0.05000248

##   DI_CENTERS SITES_CENTERS MEAN_YEARLY_DI   N_Sites
## 1  1.4839505             9      2.6275241 -8.981689
## 2  2.0423332            10      3.7641263  0.110885
## 3  0.8553333            10      1.3479576  0.110885
## 4  0.0259390            10     -0.3402957  0.110885

##   DI_CENTERS SITES_CENTERS MEAN_YEARLY_DI     N_Sites
## 1  2.1440958      9.924528      1.5649029  0.02820007
## 2  0.1493352      9.974359     -0.8156263  0.12886692
## 3  0.9258102      9.972222      0.1110118  0.12455030
## 4  1.7745536      6.750000      1.1238945 -6.38491389

K-Means Density Index Cluster Centers From 1998 to 2008 for Grand Cayman Data

	1998 Centers	2000 Centers	2002 Centers	2004 Centers	2006 Centers	2008 Centers
1	2.7750663	2.6365477	3.2500000	2.1751139	2.2421548	2.2899310
3	1.5708361	1.6000001	2.0822421	1.1793406	1.2857142	2.0802720
4	1.1111112	1.4842433	1.2232143	1.0024504	1.0686190	1.0520447
2	0.1087986	0.0764119	0.0801875	0.0391664	0.0456053	0.0446581

K-Means Density Index Cluster Centers From 2010 to 2018 for Grand Cayman Data

	2010 Centers	2012 Centers	2014 Centers	2016 Centers	2018 Centers
2	2.1001345	2.0912047	2.2011562	2.0423332	2.1440958
3	1.5784578	1.2509260	0.8624584	1.4839505	1.7745536
4	0.8914290	0.9143393	0.0654832	0.8553333	0.9258102
1	0.0759519	0.0518004	0.0000000	0.0259390	0.1493352

Specific Species Investigations

Here I will be investigating the clusters overall in terms of their centers, but also as they relate to specific species of interest in other studies.

The “Lionfish” has been shown to negatively impact reef abundance, so how has their density changed over time? The same has been shown of the Mahogony Snapper (Lutjanidae), so how has their density changed over time? (They greatly decrease grunt Haemulidae populations)

Low sighting frequencies of groupers (Serranidae), use “Yellowmouth Grouper”, “Nassau Grouper”, and “Black Grouper”, and parrotfish (Scaridae ), use “Stoplight Parrotfish”, “Redband Parrotfish”, and “Rainbow Parrotfish”, reflective of higher harvest pressure

Finally, algael abundance has been steadily increasing over the past 30 years on Grand Cayman, and studies have shown algal levels decrease at sites with high parrotfish density, but they actually increase in sites with high surgeonfish density (both are major herbivores). So, how have these fish changed in abundance over time with the increasing food supply? Is one decreasing and the other increasing?

Surgeonfish checked using: “Ocean Surgeonfish”

##   SPECIES_NAME Year cluster LF_Cluster_Center
## 1     Lionfish 1998       2        0.10879860
## 2     Lionfish 2008       3        0.04465814
## 3     Lionfish 2014       4        0.08624584
## 4     Lionfish 2018       3        0.92581020

##       SPECIES_NAME Year cluster MS_Cluster_Center
## 1 Mahogany Snapper 1998       2        0.10879860
## 2 Mahogany Snapper 2008       4        2.28993105
## 3 Mahogany Snapper 2014       4        0.08624584
## 4 Mahogany Snapper 2018       3        0.92581020

##     SPECIES_NAME Year cluster NG_Cluster_Center
## 1 Nassau Grouper 1998       3        1.57083610
## 2 Nassau Grouper 2008       3        0.04465814
## 3 Nassau Grouper 2014       4        0.08624584
## 4 Nassau Grouper 2018       3        0.92581020

##         SPECIES_NAME Year cluster RP_Cluster_Center
## 1 Rainbow Parrotfish 1998       3         1.5708361
## 2 Rainbow Parrotfish 2008       2         1.0520447
## 3 Rainbow Parrotfish 2014       3         2.2011560
## 4 Rainbow Parrotfish 2018       3         0.9258102

##        SPECIES_NAME Year cluster OS_Cluster_Center
## 1 Ocean Surgeonfish 1998       3        1.57083610
## 2 Ocean Surgeonfish 2008       3        0.04465814
## 3 Ocean Surgeonfish 2014       3        2.20115600
## 4 Ocean Surgeonfish 2018       1        2.14409580

KABLES FOR THESE SPECIES

Density Index K-Means Cluster Movements of the Lionfish

Species	Year	Cluster Classification	Cluster Center
Lionfish	1998	2	0.1087986
Lionfish	2008	3	0.0446581
Lionfish	2014	4	0.0862458
Lionfish	2018	3	0.9258102

Density Index K-Means Cluster Movements of the Mahogony Snapper

Species	Year	Cluster Classification	Cluster Center
Mahogany Snapper	1998	2	0.1087986
Mahogany Snapper	2008	4	2.2899310
Mahogany Snapper	2014	4	0.0862458
Mahogany Snapper	2018	3	0.9258102

Density Index K-Means Cluster Movements of the Nassau Grouper

Species	Year	Cluster Classification	Cluster Center
Nassau Grouper	1998	3	1.5708361
Nassau Grouper	2008	3	0.0446581
Nassau Grouper	2014	4	0.0862458
Nassau Grouper	2018	3	0.9258102

Density Index K-Means Cluster Movements of the Rainbow Parrotfish

Species	Year	Cluster Classification	Cluster Center
Rainbow Parrotfish	1998	3	1.5708361
Rainbow Parrotfish	2008	2	1.0520447
Rainbow Parrotfish	2014	3	2.2011560
Rainbow Parrotfish	2018	3	0.9258102

Density Index K-Means Cluster Movements of the Ocean Surgeonfish

Species	Year	Cluster Classification	Cluster Center
Ocean Surgeonfish	1998	3	1.5708361
Ocean Surgeonfish	2008	3	0.0446581
Ocean Surgeonfish	2014	3	2.2011560
Ocean Surgeonfish	2018	1	2.1440958